---
title: "Quantum Pulse Gate Interactive Lab | Sandbox Physics"
description: "Can choosing how to detect one photon purify its partner?"
canonical_url: "https://sandboxphysics.com/labs/quantum-pulse-gate/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/quantum-pulse-gate/"
---

FR10-B · Choose the whole pulse

# Quantum Pulse Gate

**Can choosing how to detect one photon purify its partner?** A detector that accepts one coherent pulse mode prepares its partner in a pure conditional state, provided the pair was pure. A frequency filter followed by unresolved detection can leave a mixture because several distinguishable modes still trigger the same click.

Shape the mode accepted by a herald detector and watch the partner photon change. Compare coherent selection with an intensity filter, then test a reconstructed state with a measurement kept aside.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A low-gain, pure photon pair occupies two orthonormal frequency bins. The gate uses a two-channel Schmidt conversion kernel; its optional leakage coefficient is illustrative. The model omits multipair emission, detector loss, dark counts and material propagation. Saved counts are synthetic binomial samples. Wave animation and distances are schematic.

Synthetic acquisition · saved independently of controls

## Can the saved counts predict another measurement?

Default record · 2400 samples per projection

$p_{\rm held}=\frac{1+\boldsymbol n\cdot\widehat{\boldsymbol r}}2$ $p_{\rm pred}=0.505,\quad p_{\rm obs}=0.489$

How the reconstruction uses the record

Each axis gives its positive-click fraction. Twice that fraction minus one estimates a Bloch-vector component. If sampling puts the vector outside the unit ball, radial projection restores a physical density matrix. The held-out counts do not enter this estimate.

$\widehat{\boldsymbol r}=(0,0,1)$

Physics tutorial

## Quantum Pulse Gate

**Background** Two photons leave a source together. Detecting the idler announces that its signal partner is available. The state of that partner depends on which alternatives the idler measurement combines coherently.

**Why it matters** A narrow filter throws away frequencies. A pulse gate can instead accept a superposition with a chosen relative phase, even when its components occupy a broad spectrum.

Start with the essentials

- **Focus question**: Can choosing how to detect one photon purify its partner?
- **One-sentence intuition**: A rank-one idler measurement leaves a pure signal state when the original pair is pure; the probability of that outcome is a separate question.

### Core mathematical model

#### Coherent heralding

$$
q=\begin{pmatrix}\cos\alpha\\e^{i\phi}\sin\alpha\end{pmatrix},\quad v=Fq^*,\quad p=v^\dagger v,\quad\rho_s=\frac{vv^\dagger}{p}
$$

The two components refer to orthonormal frequency bins. The idler detector accepts the mode q. Amplitudes add before the probability is calculated; a nonzero outcome leaves one normalized signal vector.

#### Unresolved intensity filtering

$$
\widetilde\rho_s=F\begin{pmatrix}\cos^2\alpha&0\\0&\sin^2\alpha\end{pmatrix}F^\dagger,\quad\rho_s=\frac{\widetilde\rho_s}{\operatorname{Tr}\widetilde\rho_s}
$$

Each transmitted idler frequency contributes a conditional signal state. The detector pools their probabilities. At the opposite pair phase and equal transmission, the result is maximally mixed.

#### A second converted mode

$$
T=\begin{pmatrix}\sqrt{\eta_0}q^\dagger\\\sqrt{\eta_1}q_\perp^\dagger\end{pmatrix},\quad\eta_k=\sin^2(g\kappa_k),\quad g=\frac\pi2
$$

The two output modes are unresolved by the herald detector. A second nonzero Schmidt coefficient adds another conditional state. This finite kernel follows the mode-coupling law of Eckstein, Brecht and Silberhorn; the leakage value here is illustrative.

### Common difficulties

#### Purity and success answer different questions

**Typical misconception** A pure conditional state means every generated pair is accepted.

**Better mental model** Purity describes accepted events. The herald probability counts how often those events occur. A setting can prepare a pure state very rarely.

### Run the experiment

1. 01

   #### Compare two kinds of selection

   Predict the purity, then compare Select a pure pulse with Pass both colors.

   **What to observe:** The coherent herald gives a pure state. With the same bin transmission weights, unresolved intensity filtering gives purity one half.

2. 02

   #### Change the phase of the gate

   Drag the gold pump dial. Its angle changes Gate relative phase; its radius changes Gate mixing.

   **What to observe:** The prepared signal mode rotates. A coherent selection can change its phase without losing purity.

3. 03

   #### Make a prediction from saved counts

   Choose Acquire projections. Change the gate, then compare the saved reconstruction with the live model before acquiring again.

   **What to observe:** The saved data stay fixed when controls move. Three projection settings reconstruct the state; the fourth setting checks a prediction and never enters the fit.

Physical conclusion

Ask what mode a click accepts, then test the prepared state with a measurement that was not used to reconstruct it.

## Related experiments and articles

Time-frequency quantum optics · Reading path

### From photon clicks to pulse-mode selection

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Preparing a partner photon by selecting one wave packet**](https://sandboxphysics.com/stories/time-frequency-quantum-optics/coherent-heralding/)
2. [Article **Reconstruct coherence from clicks and predict a new measurement**](https://sandboxphysics.com/stories/time-frequency-quantum-optics/tomography-and-holdouts/)
3. [Article **How a pulse gate approaches a single-mode measurement**](https://sandboxphysics.com/stories/time-frequency-quantum-optics/conversion-kernels/)
4. [Article **Recompute a Gaussian coherence model before reading the experiment**](https://sandboxphysics.com/stories/time-frequency-quantum-optics/paper-benchmarks/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)